There is increasing evidence to suggest that energetic particles observed in gradual solar energetic particle (SEP) events are accelerated at shock waves driven out of the corona by coronal mass ejections. Energetic particle abundances suggest too that SEPs are accelerated from in situ solar wind or coronal plasma rather than from high-temperature flare material. A dynamical time-dependent model of particle acceleration at a propagating, evolving interplanetary shock is presented here. The theoretical model includes the determination of the particle injection energy (injection here refers to the injection of particles into the diffusive shock acceleration mechanism), the maximum energy of particles accelerated at the shock, energetic particle spectra at all spatial and temporal locations, and the dynamical distribution of particles that escape upstream and downstream from the evolving shock complex. As the shock evolves, energetic particles are trapped downstream of the shock and diffuse slowly away. In the immediate vicinity of the shock, broken power law spectra are predicted for the energetic particle distribution function. The escaping distribution consists primarily of very energetic particles initially with a very hard power law spectrum (harder than that at the shock itself) with a rollover at lower energies. As the shock propagates further into the solar wind, the escaping ion distribution fills in at lower energies, and the overall spectrum remains hard. Downstream of the shock, the shape of the accelerated particle spectrum evolves from a convex, broken power law shape near the shock to a concave spectrum far downstream of the shock. Intensity profiles for particles of different energies are computed, and the relation between arrival times, maximum predicted energies, and shock propagation characteristics are described. These results are of particular importance in the context of predictive space weather studies. ¿ 2000 American Geophysical Union